Piecewise linear difference equations and convexity

This note presents a new method for analysing piecewise linear difference equations. The equations are considered in their natural phase space and interpreted via their associated semigroups and number theoretic graphs.     

Spin-selective recombination kinetics of a model chemical magnetoreceptor

We determine the spin-selective kinetics of a carotenoid-porphyrin-fullerene triad that has previously been used to establish the principle that a photochemical reaction could form the basis of the magnetic compass sensor of migratory birds and show that its magnetic sensitivity can be understood without invoking quantum Zeno effects.     

Cluster chemistry. 61. Addition of HX (XCl,Br,I) or AuCl(PPh3) to an open Ru5 cluster. X-ray structures of Ru5(μ-H)(μ5-C2PPh2)(μ-PPh2)(μ-Br)(CO)13 and Ru5(μ-H)(μ5-C2PPh2)(μ3-I)(μ-PPh2)(CO)12

Reactions of aqueous HX (X?Cl, Br) or of AuCl(PPh₃) with Ru₅(μ₅-C₂PPh₂)(μ-PPh₂)(CO)₁₃ result in addition of the 4e-donor set (H + X) or (Au(PPh₃) + Cl) with concomitant opening of two Ru? Ru bonds to give complexes containing dimetallated triangular of ‘scorpion’ cores. Aqueous HI reacts similarly, but in this case the iodide ligand spans three Ru atoms, the (H + I) set acting as 6e-donor. The structures of the two title compounds were confirmed by X-ray crystallographic studies. Ru₅(μ-H)(μ₅-C₂PPh₂)(μ-PPh₂)-(μ-Br)(CO)₁₃ is triclinic, space group P1 , a = 9.689(2), b = 11.874(2), c = 20.005(4) Å, α = 84.66(2), β = 82.90(6), λ = 67.51(6)°, Z = 2; 6478 data with I > 2σ(I) were refined to R = 0.0368, R_w = 0.0362. Ru₅(μ-H)(μ₅-C₂PPh₂)(μ₃-I)(μ-PPh₂)-(CO)₁₂.CH₂Cl₂ is monoclinic, space group P2₁/n, a = 14.809(4), b = 20.721(4), c = 17.698(5) Å, β = 111.42(2)°, Z = 4; 7815 data with I > 2σ(I) were refined to R = 0.0440, R_w = 0.0416.     

Molecule-based photonically switched half-adder

A molecule-based binary half-adder with optical inputs and outputs has been demonstrated. The half-adder consists of two photochromic organic molecules in solution and a third-harmonic-generating crystal. One substance acts as an AND Boolean logic gate and the other as an XOR gate. Inputs are laser pulses at 1064 or 532 nm that initiate photoisomerization reactions. Outputs are the optical absorbance of a fullerene radical anion (AND gate) and fluorescence of a porphyrin (XOR gate). The system carries out binary addition based on the laser input pulses. Half-adders in combination are capable of carrying out all mathematical operations necessary for digital computing.     

Nonspherical ZnS colloidal building blocks for three-dimensional photonic crystals

The asymmetry introduced by a complex or nonspherical basis promotes photonic band gap formation in three-dimensional photonic crystals. However, relatively few techniques have been demonstrated to produce uniform nonspherical colloids for use as photonic crystal bases. Here we expand the menu of basis types with high refractive index by preparing nonspherical zinc sulfide colloids of uniform size and shape. Dimers, trimers, and planar tetramers were precipitated from aqueous solution by the thermal decomposition of thioacetamide in the presence of zinc nitrate, manganese nitrate, and nitric acid. The well-defined morphological types were obtained from suspensions aged for 4-6 h at 26-32 degrees C and then for 20-35 min at 85 degrees C. Stereological techniques were used to analyze SEM images and determine the percentage of each particle class. For example, the quantitative characterization of a particle population prepared at 29 degrees C for 6 h and 85 degrees C for 22 min had the composition 59+/-3% spheres, 31+/-2% dimers, 7+/-1% trimers, 0.4+/-0.2% tetramers, and 2.5+/-0.8% complex clusters (encompasses all other varieties of shape). X-ray diffraction and X-ray photoelectron spectroscopy confirmed the zinc blend crystal structure and the stoichiometric composition of the particles. The refractive index was estimated as 2.25 (413 nm) -2.09 (709 nm) by fitting experimental absorption spectra to curves derived from Mie scattering calculations. This indicated an average porosity approximately 24%. Such colloids offer the potential to form diamond-like lattices with large, stable photonic band gaps.     

Nondestructive monitoring of the photochromic state of dithienylethene monolayers by surface plasmon resonance

The use of surface plasmon resonance (SPR) as a nondestructive, nonerasing readout of the isomerization state of a photochromic dithienylethene covalently linked to a chemically modified gold surface was investigated. Four different binding layers were examined: 11-mercaptoundecanol (MUO), an amine-modified 11-mercaptoundecanol (MUO-NH2), dextran, and an amine-modified dextran. The binding of dithienylethene to the modified gold surface and photoisomerization of the photochrome in the bound state were established by FTIR. Solvent effects were measured for every layer tested using ethanol and hexanes. In general, large, easily measurable SPR signal changes could be detected under conditions where photoisomerization of the dithienylethene photochrome was not quenched by the gold plasmon, establishing SPR as a viable form of readout for potential dithienylethene-based optical data storage or processing devices. Dextran-bound photochrome in ethanol exhibited the largest SPR response upon photoisomerization, but is more prone to time-dependent fluctuations resulting from swelling of the dextran layer (caused by slow diffusion of the solvent) than the other layers. Large responses are also provided by MUO-NH2 and MUO, and the signal is much more stable than that for dextran.     

Carotenohematoporphyrins as Tumor-Imaging Dyes. Synthesis and In Vitro Photophysical Characterization*

Multichromophoric dyes for use in tumor imaging have been synthesized and photophysically characterized. Structurally, these dyes are dyads and triads that consist of one or two carotenoid polyenes covalently attached to hematoporphyrin (HP) or hematoporphyrin dimethyl ester (HPDME) moieties via ester linkages. The ground-state absorption of each compound shows that the electronic interaction between the chromophores is small. The fluorescence quantum yield for the dyad monocar-oteno- HPDME is 0.033 and the dicaroteno-HPDME triads have yields between 0.016 and 0.007, all of which are reduced with respect to the parent compound HPDME (0.09). Global analysis of the transient fluorescence decays of the dyads and triads requires two exponential components (?5–6ns and ?1–2ns) to fit the data, while a single exponential component with a lifetime of 9.3 ns describes the decay data of the parent HPDME. Possible mechanisms for the observed porphyrin fluorescence quenching by the nearby carotenoid are discussed. Nanosecond transient absorption reveals a carotene triplet with maximum absorption at 560 nm and a 5.0 μs lifetime. No transient was detected at 450 nm, indicating rapid (10 ns) triplet energy transfer from the hematoporphyrin to the carotenoid moieties in fluid as well as in rigid media. The yield of triplet energy transfer from the porphyrin to the carotenoid moiety is unity. Singlet oxygen, O₂(¹δ_g), studies support the transient absorption data, as none of these compounds is capable of sensitizing O₂(¹δ_g). Liposome vesicles were used to study the photophysical characteristics of the dyes in phospholipid membranes. Singlet oxygen was not sensitized by the dyads and triads in liposomes. Transient absorption measurements suggest that the triads are substantially aggregated within the phospholipid bilayer, whereas aggregation in the dyads is less severe.     

Pyrrolizidine alkaloids

This review covers a range of pyrrolizidine alkaloids which have been isolated from various natural sources. The synthesis of necines and necic acids is described along with pharmacological and biological studies of pyrrolizidine alkaloids. The literature from July 2000 to June 2001 is reviewed, and 59 references are cited.